This invention generally concerns nuclear reactor fuel-cycle design and management.
A nuclear reactor core includes many individual components that have different characteristics that may affect a strategy for efficient operation of the core. For example, a nuclear reactor core has many, e.g., several hundred, individual fuel assemblies (bundles) that have different characteristics and which must be arranged within the reactor core or xe2x80x9cloadedxe2x80x9d so that the interaction between fuel bundles satisfies all regulatory and reactor design constraints, including governmental and customer specified constraints. Similarly, other controllable elements and factors that affect the reactivity and overall efficiency of a reactor core must also be taken into consideration if one is to design or develop an effective control strategy for optimizing the performance of a reactor core at a particular reactor plant. Such xe2x80x9coperational controlsxe2x80x9d (also referred to herein as xe2x80x9cindependent control-variablesxe2x80x9d) include, for example, various physical component configurations and controllable operating conditions that can be individually adjusted or set. Besides fuel bundle xe2x80x9cloadingxe2x80x9d, other sources of control variables include xe2x80x9ccore flowxe2x80x9d or rate of water flow through the core, the xe2x80x9cexposurexe2x80x9d and the xe2x80x9creactivityxe2x80x9d or interaction between fuel bundles within the core due to differences in bundle enrichment, and the xe2x80x9crod patternxe2x80x9d or distribution and axial position of control blades within the core. As such, each of these operational controls constitutes an independent xe2x80x9ccontrol-variablexe2x80x9d that has a measurable effect on the overall performance of the reactor core. Due to the vast number of possible different operational values and combinations of values that these independent control-variables can assume, it is a formidable challenge and a very time consuming task, even using known computer-aided methodologies, to attempt to analyze and optimize all the individual influences on core reactivity and performance.
For example, the number of different fuel bundle configurations possible in the reactor core can be in excess of one hundred factorial. Of the many different loading pattern possibilities, only a small percentage of these configurations will satisfy all of the requisite design constraints for a particular reactor plant. In addition, only a small percentage of the configurations that satisfy all the applicable design constraints are economically feasible. Moreover, in addition to satisfying various design constraints, since a fuel bundle loading arrangement ultimately affects the core cycle energy (i.e., the amount of energy that the reactor core generates before the core needs to be refueled with new fuel elements), a particular loading arrangement needs to be selected that optimizes the core cycle energy.
In order to furnish and maintain the required energy output, the reactor core is periodically refueled with fresh fuel bundles. The duration between one refueling and the next is commonly referred to as a xe2x80x9cfuel-cyclexe2x80x9d or xe2x80x9ccore-cyclexe2x80x9d of operation and, depending on the particular reactor plant, is on the order of twelve to twenty-four (typically eighteen) months. At the time of refueling, typically one third of the least reactive fuel are removed from the reactor and the remaining fuel bundles are repositioned before fresh fuel bundles are added. Generally, to improve core cycle energy higher reactivity bundles should be positioned at interior core locations. However, such arrangements are not always possible to achieve while still satisfying plant-specific design constraints. Since each fuel bundle can be loaded at a variety of different locations relative to other bundles, identifying a core loading arrangement that produces optimum performance of the core for each fuel-cycle presents a complex and computation-intensive optimization problem that can be very time consuming to solve.
During the course of a core-cycle, the excess energy capability of the core, defined as the excess reactivity or xe2x80x9chot excessxe2x80x9d, is controlled in several ways. One technique employs a burnable reactivity inhibitor, e.g., Gadolinia, incorporated into the fresh fuel. The quantity of initial burnable inhibitor is determined by design constraints and performance characteristics typically set by the utility and by the NRC. The burnable inhibitor controls most, but not all, of the excess reactivity. Consequently, xe2x80x9ccontrol bladesxe2x80x9d (also referred to herein as xe2x80x9ccontrol rodsxe2x80x9d)xe2x80x94which inhibit reactivity by absorbing nuclear emissionsxe2x80x94are also used to control excess reactivity. Typically, a reactor core contains many such control blades which are fit between selected fuel bundles and are axially positionable within the core. These control blades assure safe shut down and provide the primary mechanism for controlling the maximum power peaking factor.
The total number of control blades utilized varies with core size and geometry, and is typically between 50 and 150. The axial position of the control blades (e.g., fully inserted, fully withdrawn, or somewhere in between) is based on the need to control the excess reactivity and to meet other operational constraints, such as the maximum core power peaking factor. For each control blade, there may be, for example, 25 or more possible axial positions and 25 xe2x80x9cexposurexe2x80x9d (i.e., duration of use) steps. Considering symmetry and other requirements that reduce the number of control blades that are available for application at any given time, there are more than 6 million possible combinations of control blade positions for even the simplest case. Of these possible configurations, only a small fraction satisfy all applicable design and safety constraints, and of these, only a small fraction are economical. Moreover, the axial positioning of control blades also influences the core cycle energy that any given fuel loading pattern can achieve. Since it is desirable to maximize the core-cycle energy in order to minimize nuclear fuel cycle costs, developing an optimum control blade positioning strategy presents another formidable independent control-variable optimization problem that must also be taken into consideration when attempting to optimize fuel-cycle design and management strategies.
Traditionally, reactor fuel-cycle design and management, including core loading and control blade positioning determinations as well as optimization strategies concerning other variable operational controls, are determined on a xe2x80x9ctrial-and-errorxe2x80x9d basis based primarily on the past experiences of the reactor core design engineers. Due to circumstances that require a rapid response to changing plant operating conditions, a core design engineer may be faced with the formidable challenge of specifying values for over 200 independent control-variables within a very short time frame. The impact, for example, of a particular suggested core loading arrangement or a control blade positioning arrangement on reactor performance over the duration of a core-cycle is usually determined by individual computer simulations. If a particular design constraint is not satisfied by an identified arrangement, then the arrangement is modified and another computer simulation is run. Because of the relatively long computer simulation time required for assessing the impact of a change in the value of even a single given independent control-variable, man-weeks of human and computer resources are typically required before an appropriate fuel-cycle design is identified using this procedure. Moreover, using this trial-and-error approach, once a fuel-cycle design arrangement that satisfies all design and safety constraints has been identified, it may turn out that the identified arrangement may not provide the actual maximum cycle-energy. Therefore, this trial-and-error process must continue until the engineers believe that an optimum fuel-cycle design for the core has been identified. In practice, however, it is very possible that a particular core arrangement that is not consistent with the engineers"" past experience may be the actual optimum fuel-cycle design for the core. Such an actual optimum core arrangement, however, may not necessarily be identified through the above described trial and error process.
Since operational control strategy problems generally are considered unique to each reactor plant, no known algorithm has provided a viable solution for identifying optimum operational control strategies. In addition, expert systems have not been applied on a broad basis since a standard set of rules typically are not really applicable over the wide range of situations characteristic of the many different reactor plants and types currently in commercial operation. Few methodologies have been developed which can significantly reduce the time required to identify a fuel bundle loading arrangement or identify a control blade positioning arrangement that optimizes cycle energy and satisfies design constraints for a wide range of reactors. At least one methodology applicable to a wide range of reactors for identifying optimum control blade positioning arrangements was developed and is the subject of commonly assigned U.S. Pat. No. 5,790,616 to Jackson, issued Aug. 4, 1998.
Similar methodologies have been developed for identifying optimum core fuel bundle loading arrangements. See, for example, commonly assigned U.S. Pat. No. 5,923,717 to Fawks, Jr., issued Jul. 13, 1999 and U.S. Pat. No. 5,790,618 to Fawks, Jr., issued Aug. 4, 1998. For the most part, the above methodologies employ a single processor or computer system to execute a specific program routine that simulates the reactor operating conditions under a selected component arrangement/configuration of fuel bundle locations or control blade axial positions and then the arrangement is optimized by systematically or stochastically evaluating possible alternatives. Subsequent to analyzing each position or location, random arrangements are created and compared with the then best case arrangement identified. Another example is a recent methodology for boiling water reactor (BWR) incore fuel management optimization that uses a 3-D core simulation computer program called FORMAOSA-B. (See xe2x80x9cFORMOSA-B: A BWR Incore Fuel Management Optimization Packagexe2x80x9d by B. R. Moore, P. J. Turinski and A. A. Karve, Nuclear Technology, 126, 153 (1999)). An enhanced version of the FORMAOSA-B code has a limited fuel loading pattern optimization capability through the use of a stochastic optimization technique called xe2x80x9csimulated annealingxe2x80x9d. (See the paper entitled xe2x80x9cEffectiveness of BWR Control Rod Pattern Sampling Capability in the Incore Fuel Management Code FORMOSA-Bxe2x80x9d by A. A. Karve and P. J. Turinski presented at the conference on xe2x80x9cMathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Application,xe2x80x9d published September 1999, SENDA EDITORIAL, S.A.).
Unfortunately, the above-described methodologies are only applicable for optimizing a single or a few operational control-variables at a time such as, for example, fuel bundle loading pattern or control blade position. Moreover, the above methodologies fail to address the optimization of other important operational control-variables such as fuel bundle enrichment, blade sequence interval, core water flow, and other independent control-variables that may also be critical to quality and performance. Consequently, it would be highly desirable to have an efficient optimization methodology and apparatus that is broadly applicable over a wide range of reactor plant types and which is capable of identifying the best possible fuel-cycle core design and in-core fuel management strategy in light of all the intrinsic operational control-variables as well as the many different specific constraints and considerations that may be critical to quality for the operation of a particular reactor plant.
An embodiment of the present invention provides a system and method for optimizing multiple operational control-variables of a nuclear reactor to identify an optimum fuel-cycle design and develop an operational management strategy. In one aspect, the present invention is a networked computer system including one or more computers programmed to execute a nuclear reactor simulation program and having at least one computer programmed to determine the most appropriate values for selected control-variables that result in the optimal physical configuration for operating the reactor core over one or more refueling cycles. In another aspect, the present invention is a method for efficiently determining optimized values for the operational control-variables that effect the performance of a nuclear reactor corexe2x80x94an operational control-variable being the xe2x80x9ccontrollablexe2x80x9d physical aspects of the reactor, such as fuel bundle loading, control rod pattern, core flow, etc., the characteristics of which define the physical configuration and operational constraints of a particular reactor core. Rather than relying on random or stochastic search techniques or rule-based techniques in an attempt to reduce the size of the xe2x80x9csearchxe2x80x9d space, the optimization method of the present invention performs a deterministic and exhaustive -search for an optimum solution.
In an example embodiment of the invention, a plurality of several thousand performance parametersxe2x80x94also referred to herein as xe2x80x9cdependentxe2x80x9d variables because of their dependence upon the setting or values of the various operational control-variablesxe2x80x94are utilized as a measure of determining reactor core performance. These xe2x80x9cperformance parametersxe2x80x9d include but are not limited to parameters conventionally used to gauge reactor core performance, such as critical power ratio (CPR), shutdown margin (SDM), maximum average linear heat generation rate (MAPLHGR), maximum fraction of linear power density (MFLPD), Hot excess, etc. Many of the performance parameters analyzed are both spatially and time dependent, such as, for example, MAPLHGR, MFLPD, and minimum critical power ratio (MCPR). Consequently, the present invention must be capable of analyzing several thousands of such xe2x80x9cdependentxe2x80x9d variables. To accomplish this, an exemplary embodiment of the present invention utilizes a plurality of processors to conduct separate computer simulations covering the operation of the reactor core throughout one or more fuel cycles to determine how changes to many different control-variables affect the performance of the core as measured by the respective performance parameters. Preferably, these reactor core simulations are conducted utilizing a computer program capable of performing three-dimensional (3-D) physics modeling of reactor core operation (i.e., the simulator program should be capable of handling three-dimensional control variables).
The method of the present invention significantly decreases the number of required simulationsxe2x80x94and hence increases the overall computational efficiencyxe2x80x94by mapping the results of a relatively few number of reactor core computer simulations to second-order polynomials. The polynomials are then subsequently used to predict quantitative values for performance parameters (i.e., the dependent variables) over a selected limited range (i.e., xe2x80x9cbreadthxe2x80x9d) of quantitative values or settings for one or more selected control-variables (i.e., the independent variables). Consequently, each polynomial xe2x80x9cpredictorxe2x80x9d effectively saves the processing time that would be required to actually run computer simulations for the many discrete quantitative values that a particular control-variable might assume within a selected range or xe2x80x9cbreadthxe2x80x9d of possible control-variable values. Each of these polynomial predictors are defined in terms of a unique set of coefficient values that are stored in a multidimensional data array in a host computer memory. In this manner, the data array serves as a type of virtual xe2x80x9cresponse surfacexe2x80x9d for cataloging and analyzing the results of many different simulation cases, based on a 3-D physics modeling of the core, in terms of polynomials indicative of reactor performance that are represented by the polynomial coefficients.
Using the polynomial predictors, quantitative values for performance parameters are determined for discreet control-variable values at selected predetermined increments over the breadth of possible values for each control-variable. Each performance parameter value is then compared using a conventional xe2x80x9cobjective functionxe2x80x9d, which sets limiting values for each performance parameter, to determine the best set of control-variable polynomial predictors for optimizing core performance. As an option, a particular optimization xe2x80x9cresolutionxe2x80x9d level may be selected wherein the combined effect of a change in two or more control-variables is analyzed. In that instance, predicted values for the two or more performance parameters are combined to generate a net-change or xe2x80x9csuperpositionxe2x80x9d value indicative of the core simulation that would likely result. A corroborating reactor core simulation is then conducted using the best predicted value(s) obtained for each control-variable to provide corroboration of the polynomial predictors and to calibrate the polynomial coefficient data in the response surface with the simulation process.
The method of the invention presented herein can be practiced using most any type of computer network or interconnected system of processors having sufficient processing speed and associated data storage capacity and is not necessarily intended to be limited to any particular type of data processor or network. Moreover, the software system of the present invention, including one or more software modules, may be embodied on a computer-readable medium for transport between and/or installation on one or more processors/computers or networked computer systems. In addition, the method and system presented herein are believed to be applicable toward optimizing the fuel-cycle design and operation of many different types of reactor plants including both boiling water reactors (BWRs) and pressurized-water reactors (PWRs).